We propose that the carbon dimer defect in hexagonal boron nitride gives rise to the ubiquitous narrow luminescence band with a zero-phonon line of 4.08 eV (usually labeled the 4.1 eV band). Our first-principles calculations are based on hybrid density functionals that provide a reliable description of wide band-gap materials. The calculated zero-phonon line energy of 3.8 eV is close to the experimental value, and the deduced Huang-Rhys factor of \({S \approx 2.0}\), indicating modest electron-phonon coupling, falls within the experimental range. The optical transition occurs between two localized \(\pi\)-type defects states, with a very short radiative lifetime of 1.7 nanoseconds, in very good accord with experiments.